Crocheting Adventures with Hyperbolic Planes

With more than 200 full color photographs, this non-traditional, tactile introduction to non-Euclidean geometries also covers early development of geometry and connections between geometry, art, nature, and sciences. For the crafter or would-be crafter, there are detailed instructions for how to crochet various geometric models and how to use them in explorations. From the Foreword by William Thurston: ''These models have a fascination far beyond their visual appearance. As illustrated in the book, there is actually negative curvature and hyperbolic geometry all around us, but people generally see it without seeing it. You will develop an entirely new understanding by actually following the simple instructions and crocheting! The models are deceptively interesting. Perhaps you will come up with your own variations and ideas. In any case, I hope this book gives you pause for thought and changes your way of thinking about mathematics.'' This Richly Illustrated Book Discusses Non-euclidean Geometry And The Hyperbolic Plane In An Accessible Way. The Author Provides Instructions For How To Crochet Models Of The Hyperbolic Plane, Pseudosphere, And Catenoid/helicoids. With This Knowledge, The Reader Has A Hands-on Tool For Learning The Properties Of The Hyperbolic Plane And Negative Curvature. The Author Also Explores Geometry And Its Historical Connections With Art, Architecture, Navigation, And Motion, As Well As The History Of Crochet, Which Provides A Context For The Significance Of A Physical Model Of A Mathematical Concept That Has Plagued Mathematicians For Centuries.--publisher Description. Introduction -- What Is The Hyperbolic Plane? Can We Crochet It? -- What Can You Learn From Your Model? -- Four Strands In The History Of Geometry -- Tidbits From The History Of Crochet -- What Is Non-euclidean Geometry? -- How To Crochet A Pseudosphere And A Symmetric Hyperbolic Plane -- Metamorphoses Of The Hyperbolic Plane -- Other Surfaces With Negative Curvature : Catenoid And Helicoid -- Who Is Interested In Hyperbolic Geometry Now And How Can It Be Used? -- Paper Models. Daina Taimiņa. Includes Bibliographical References (p. 139-144) And Index. Crocheting Adventures with Hyperbolic Planes is a work of gargantuan proportions whose influence will be measured for decades to come. Delightfully brilliant yet down to earth, Daina Taimina brings together the best aspects of right brain imagination and risk-taking with left brain facts, practicality, and pattern perception, creating a win-win situation that everyone will enjoy. Lavish with photos throughout the book, the art is creatively placed in nature and the math schematics are crisp and clear. This book is a must for the bookshelves of crochet. Introduction What is the hyperbolic plane? Can we crochet it? What can you learn from your model? Four strands in the history of geometry Tidbits from the history of crochet What is non-Euclidean geometry? How to crochet pseudosphere and hyperbolic plane from the center Metamorphoses of the hyperbolic plane Other surfaces with negative curvature Who is interested in hyperbolic geometry now and how can it be used? Paper models. Discusses non-Euclidean geometry and the hyperbolic plane. This book provides instructions for how to crochet models of the hyperbolic plane, pseudosphere, and catenoid/helicoids. It explores geometry and its historical connections with art, architecture, navigation, and motion, as well as the history of crochet.